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Multidimensional scaling

Multidimensional scaling. Research Methods Fall 2010 Tamás Bőhm. Multidimensional scaling (MDS). Earlier methods: measuring the properties of one specific perceptual dimension ( e.g. brightness, pitch ) Simple stimuli with one physical dimension varied S pot of light, pure tones etc.

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Multidimensional scaling

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  1. Multidimensional scaling Research Methods Fall 2010 Tamás Bőhm

  2. Multidimensional scaling (MDS) • Earlier methods: measuring the properties of one specific perceptual dimension(e.g. brightness, pitch) • Simple stimuli with one physical dimension varied Spot of light, pure tones etc. • MDS: exploring what the perceptual dimensions are • Complex stimuli with multiple dimensions Faces, melodies, etc. • Perceptual maps are created from similarity judgments

  3. Multidimensional scaling • What does the MDS algorithm do? From a matrix of distances… Kruskal & Wish, 1978

  4. Multidimensional scaling • What does the MDS algorithm do? …it calculates a map…

  5. Multidimensional scaling • What does the MDS algorithm do? …but it cannot tell the orientation and the meaning of the axes.

  6. Multidimensional scaling Experiment setup • Present the stimuli pair-wise and ask the observer how similar they are(e.g. on a 0-100 scale) • Create the dissimilarity matrix • Run MDS to get a perceptual map of the stimuli • Interpret the dimensions of the map

  7. Stimuli: 4 different salt concentrations(A: 0.5%, B: 2%,C: 1%, D: 1.5%) Dissimilarity judgments (0: perfect similarity;100: no similarity) A vs B: 90 A vs C: 10 A vs D: 55 B vs C: 80 B vs D: 35 C vs D: 45 Dissimilarity matrix Multidimensional scaling Symmetrical(i.e. A vs B = B vs A)

  8. Multidimensional scaling • Perceptual map: each stimuli represents a point, their distances correspond to dissimilarities A C D B 1D solution

  9. Multidimensional scaling • Interpreting the dimensions: looking for correspondences between physical and perceptual dimensions B D Dimension 1(from MDS) Dimension 1: intensity of salt taste C A Salt concentration

  10. Another example: soft drinks Multidimensional scaling

  11. Multidimensional scaling Diet taste 20 Pepsi Diet Pepsi 10 10 20 Coke Diet Coke 30 30 Cherry Coke Diet Cherry Coke 20 Cherry taste 2D solution

  12. Multidimensional scaling Shepard, 1963: • Morse-codes presented in pairs to naïve observers (each possible combination) • Same/different task • Confusion matrix (% same responses): can be interpreted as a dissimilarity matrix

  13. Multidimensional scaling Jacobowitz (see Young, 1974): • Children and adults judged the similarity of all pairs of 15 parts of the human body • Task: rank ordering of similarity to a standard  dissimilarity matrix

  14. Multidimensional scaling 7-year-olds adults

  15. Multidimensional scaling • Hair (long/short) • Jaw(smooth/rugged) • Eye (bright/dark)

  16. Multidimensional scaling Additional perceptual dimension revealed

  17. Multidimensional scaling

  18. Multidimensional scaling • Directly asking about the perceptual dimensions: • requires prior knowledge • introduces bias • MDS: • no prior assumptions about the possible dimensions (exploratory) • no response bias • Reveals the hidden structure of the data • MDS is about relationships among stimuli(does not tell us about the perception of individual entities)

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